Jumping Champions

Author

Eric W. Weisstein
February 16, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PrimeNumbers/JumpingChampions.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/JumpingChampions.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Champions

JumpingChampion[n_]:=Module[{l=Split[Sort[-Subtract@@@Partition[Prime/@Range[1,PrimePi[n]],2,1]]]},
First/@Select[l,Length[#]==Max[Length/@l]&]
]

Table[{#,JumpingChampion[#]}&[Prime[n]],{n,100}]//ColumnForm

Plot

jump=Table[JumpingChampion[Prime[n]],{n,10000}];
u=Union[Flatten[jump]]

l=First/@(Position[jump,#,{0,Infinity},1][[1]]&/@u)

Prime/@l

GraphicsGrid[{ListPlot[Flatten[Table[{n,#}&/@JumpingChampion[Prime[n]],{n,#}],1],AxesLabel->{n,j[(Subscript[p, n])]},PlotStyle->Red]&/@{100,1000}},ImageSize->500]